FIN.5:4 - Solution

1. Match the claim and the cash flows. Identify operating cash available to all capital providers, cash available to common equity, or another specified claim. Fix currency, valuation date, timing, inflation and tax basis. FIN.4 supplies the projection; FIN.6 excludes financing payments from the operating cash flows discounted at WACC. Recover the debt policy from the financing terms and supported plan: which amounts are fixed or repaid, and when borrowing is reset to market value. Establish how the resulting interest deductions are used and priced before selecting a beta-transfer model below.

2. Choose a return model for that use. One route for equity is CAPM: required equity return = risk-free return + equity beta × market equity premium. Beta measures how the equity return varies with the chosen market’s return; it is not the probability of project failure. This model prices exposure to market risk for a diversified investor. Use the fuller construction below when estimating its inputs. A private company may use comparable listed businesses, but concentrated ownership, market access and the valuation’s purpose can require another supported return model or valuation adjustment. Establish that basis before adding a “private-company premium”; CFA’s private-company discussion identifies these differing circumstances. If a needed adjustment is unsupported, return a conditional estimate and name the missing evidence.

3. Estimate a current debt return for comparable borrowing. Start from current traded debt or obtainable terms with matching currency, maturity, security and priority. Separate the benchmark rate from the credit spread; explain which issuer and financing conditions make that spread relevant. The coupon on an old loan need not be today’s borrowing cost. A yield based on promised payments can approximate the required expected return when expected default losses are immaterial; otherwise estimate expected receipts and losses consistently with the valuation model. FIN.10 supplies net proceeds, fees and actual payment terms for an issue comparison. A one-off issue fee belongs in that financing comparison or its explicit valuation effect, rather than silently becoming a perpetual debt spread.

4. Combine matching returns and financing weights. For the matched debt-and-common-equity model, WACC = E/(D+E) × required equity return + D/(D+E) × debt return × (1−usable marginal tax rate). E and D are market values of the claims, or a justified prospective market-value mix supplied by FIN.11. For traded equity, price times the relevant share count supplies a starting value. For untraded claims, use FIN.7’s valuation for the identified interest or an adequate supplied value; carry a material valuation range into the weights. Other claims require their own weights and treatment. Book amounts are usable proxies only with a reason they approximate the needed values. The tax adjustment requires applicable deductibility, timely usability and the financing/tax-shield model used in the risk transfer.

5. Value financing under the selected policy. Use the peer’s and project’s own policy assumptions in the construction below. A fixed debt amount, a repayment schedule and a repeatedly restored market-value share can require different valuations. For a schedule outside the supported constant-WACC case, use adjusted present value: discount operating cash flows at the unlevered required return, then add the present value of usable financing benefits and subtract financing costs, including relevant distress effects. Calculate the tax savings on the actual debt and deduction schedule; price their risk explicitly. Do not also include those same benefits in an after-tax WACC. The APV explanation and worked valuation develop the separate-effects approach. If weights depend on the resulting value, reconcile those values and weights. FIN.12 supplies the access constraints.

6. Return a usable estimate and its sensitivity. Give the rate or range, the claim and cash-flow basis it supports, the relied-on inputs and dates, and the assumptions whose change would alter the decision. Propagate plausible changes into FIN.6–8’s valuation. If they reverse the choice, report that dependence and obtain the missing estimate or compare a conditional action. Keep the estimated investor return, management’s chosen project-acceptance minimum and the quoted borrowing offer distinct.

Understand what the required return represents

Capital committed here cannot simultaneously be used in an available alternative of comparable risk. The required return represents that opportunity cost in the selected valuation model. It is not an extra payment appearing in the operating cash account, a promise that the project will earn that amount, or management’s wish for a larger margin of safety. NPV tests whether the projected cash more than compensates for that opportunity cost.

In CAPM, the additional compensation concerns the claim’s co-movement with the market opportunity set for a diversified investor. A firm-specific failure can still reduce expected receipts even where that particular risk earns no separate market premium. Model the failure’s consequences in expected cash; do not treat “diversifiable” as “cannot lose money.” Conversely, a large spread of possible outcomes does not by itself identify the beta or required premium.

Identify how risk is represented before changing either cash or the rate. Expected cash already includes unfavorable outcomes with their supported probabilities. A market-risk premium applied to those expected flows is not automatically double counting: the expected loss and the price of bearing its covariance risk are different effects. Double counting occurs when the same compensation for risk has already been deducted in a certainty-equivalent cash amount and is charged again through a risk-adjusted rate. A deliberately conservative management scenario is neither automatically an expectation nor a certainty equivalent.

A low borrowing offer does not make operating risk disappear. Lenders and equity holders have different claims on the same business, and a guarantee can shift who bears a loss without eliminating its cost. A subsidy or concession can have value, but identify the resulting financing benefit and its conditions separately. Do not replace the entire project’s required return with the subsidized loan’s coupon.

The applicable investor and valuation purpose matter. A traded diversified-investor valuation and a particular undiversified owner’s reservation value need not use the same risk preferences or model. Identify that change through FIN.1 and obtain the appropriate supported approach. Adding several unexplained premiums for size, private ownership, country and “project uncertainty” can charge overlapping effects without establishing any of them.

Build the risk-free return and market premium

Obtain a default-free benchmark in the cash-flow currency at the valuation date. Its maturity or term structure should match the cash-flow horizon: a short bill repeatedly rolled over does not fix a long-term return. Where maturity differences matter, use the relevant zero-coupon curve and dated discount factors. A government yield containing material default risk needs an explicit adjustment or another supported benchmark. Real cash flows need a real return basis. The risk-free-rate explanation develops these matching choices.

Choose an equity premium for the same market and benchmark convention. A historical estimate compares equity total returns with the specified risk-free returns over a stated period; the period and averaging convention affect it. An implied estimate solves for the return consistent with the current market price and forecast distributions, then subtracts the matched risk-free return. It depends on the forecast and pricing model. Compare defensible estimates when the choice matters; a historical average is not an observed future premium. The estimation discussion explains the trade-offs.

Match business exposure to the project

A corporate average is usable for a project only insofar as the valued activity and financing assumptions are comparable. Investigate the economic sources of exposure: what moves demand and prices, which costs can adjust, which payments are fixed, what customers or suppliers concentrate risk, and how contracts or regulation alter the response. A familiar industry label alone does not establish the same exposure.

For a corporation with several activities, use the relevant business contribution rather than the average exposure of unrelated divisions. The bottom-up construction below allows a project without traded equity to use evidence from comparable activities. A new project serving different customers or operating with a materially different cost structure may need its own comparison. Explain the difference before deciding that finer estimation is worthwhile; numerical precision cannot rescue an economically poor peer.

Distinguish the uncertainty of the estimate from the underlying investment risk. An imprecisely estimated beta is a reason to inspect the sample, compare an alternative estimate or carry a range. Raising the central rate merely because the analyst is unsure does not identify the price of the actual risk. A larger peer set can reduce some estimation noise while introducing less comparable activities, and common source errors do not vanish through averaging.

Account for changes in business mix, contract protection and operating conditions over the valued horizon. A past regression can describe exposure that the proposed operation no longer has. In a cross-border activity, currency matching does not by itself settle the risk of customer demand, enforceability, restrictions or transfer of proceeds. Model the relevant operating and payment consequences and obtain an evidenced risk treatment; place of incorporation alone does not determine a universal surcharge.

Retain the economic reason for the chosen estimate so that a changed project can be reassessed. A rate copied without that reason gives the next analyst no way to tell whether a larger plant, a long-term offtake agreement or a different customer group changes the basis.

Recover business risk before transferring a beta

For a listed comparable business, obtain aligned stock and market total returns, including distributions, for the same periods. Subtract each period’s risk-free return to obtain excess returns. If x is market excess return and y is the claim’s excess return, estimate beta as Σ[(x−mean x)×(y−mean y)] / Σ[(x−mean x)²]. This is the regression slope. The same calculation can estimate a traded debt claim’s beta when suitable return data exist. Alternatively, obtain an estimate with those definitions. Examine the window, market benchmark, infrequent trading and business changes before using it.

Choose peers for their operating exposure and establish the financing policy underlying each estimate. Use financial statements, repayment terms and supported refinancing assumptions to distinguish a fixed amount from a market-value target and its reset dates. Then select the project’s forward policy from FIN.10–11. A matching current D/E ratio alone does not establish a matching policy.

Let a express the financing model’s adjustment in the following relations. Two illustrative choices are:

The permanent-debt case values its recurring tax savings at t×D. Annual resetting fixes only the coming year’s borrowing; subsequent amounts depend on business value. Both models require usable deductions and treatment of additional financing frictions. The examples below stipulate proportional loss-sharing and tax-exempt debt cancellation, with the deductions priced at the expected debt return. With risky debt, verify those loss and tax conditions; another treatment can change the tax-shield discount rate. The policy derivation, especially equation 11 and footnote 9, explains those conditions. A finite fixed loan does not satisfy the permanent-debt premise; use its dated financing effects in step 5. If the actual policy or shield risk is unsupported, obtain that basis or keep the valuation conditional.

For each peer, remove its financing effect as βU = [βE + βD×a×D/E] / [1 + a×D/E]. Apply the target’s own factor and debt estimate as βE = βU + (βU−βD)×a×D/E. Here βU is unlevered business beta, βE equity beta and βD debt beta. Set βD to zero only when negligible debt market risk is a justified approximation.

Combine relevant business estimates only after removing their financing effects. Material excess cash or a different business mix needs separation; revenue weights need not equal business-value weights. Use a supported debt-beta estimate or a range when debt risk matters. The fuller bottom-up-beta treatment develops peer selection and combination; the policy choice above qualifies its tax-adjusted transfer. Compare the resulting valuations when more than one financing policy remains plausible. An approximation cannot settle the decision when the supported alternatives change its result.

Use discount factors and financing effects on compatible grounds

A single annual rate is a useful compression only when the valued cash and financing model support it. For deterministic annual forward discount rates r1 through rt, the discount factor to time t is 1/[(1+r1)×…×(1+rt)]. A time-t spot rate zt instead gives 1/(1+zt)^t. Do not treat a quoted spot rate as a one-year forward rate and compound both adjustments. For risky cash, use the corresponding supported pricing factors or model; the risk-free term structure alone does not supply them.

When risk changes over time, identify which remaining claim is exposed to which conditions before selecting its pricing model. A fixed contractual payment, an uncertain operating receipt and an exercisable option can have different risks even when they occur on the same date. Value materially different components on their matched grounds and combine their present values. FIN.8 supplies the changing contingent payoff of an option.

For a certainty-equivalent approach, obtain the amount certain at each date that has the same value as the risky claim, then discount that amount using the matching risk-free factors. The risk adjustment needs a supported model; a discretionary haircut is not enough. For an expected-cash approach, use the required expected-return model that prices those cash flows. Keep the two representations distinct through the calculation.

Do not apply an increasing “risk rate” indiscriminately to unavoidable future costs. A higher positive discount rate reduces the present magnitude of a negative payment and can make an adverse obligation appear cheaper. Establish the payment’s own risk and timing. Similarly, a bond yield computed from promised payments includes a different relationship between price, default losses and receipts from a required return computed on expected payments. When losses matter, obtain the expected payment/recovery account and its matching pricing basis rather than transferring the promised yield unchanged.

APV is especially useful when the financing schedule must remain visible. It separates operating value from the usable deductions, subsidies, issue costs and other financing effects that change value. Value each effect once with its own timing and risk. Adding a distress estimate already included through lost customers or recovery flows would count that consequence twice. Omitting such effects merely because a tax-shield calculation is precise would overstate the benefit of borrowing.

Finally propagate a defensible range into the receiving decision. In the worked case below, a tiny rate difference changes the NPV sign. More displayed decimals cannot settle uncertain debt policy or business comparability. Return the rate’s grounds and the condition that would change the choice; FIN.11 decides the financing mix and FIN.12 determines what can actually be obtained.